TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Hounnon, Hippolyte
T1  - Partial Menger algebras of terms
JF  - Asian-European journal of mathematics
N2  - The superposition operation S-n,S-A, n >= 1, n is an element of N, maps to each (n + 1)-tuple of n-ary operations on a set A an n-ary operation on A and satisfies the so-called superassociative law, a generalization of the associative law. The corresponding algebraic structures are Menger algebras of rank n. A partial algebra of type (n + 1) which satisfies the superassociative law as weak identity is said to be a partial Menger algebra of rank n. As a generalization of linear terms we define r-terms as terms where each variable occurs at most r-times. It will be proved that n-ary r-terms form partial Menger algebras of rank n. In this paper, some algebraic properties of partial Menger algebras such as generating systems, homomorphic images and freeness are investigated. As generalization of hypersubstitutions and linear hypersubstitutions we consider r-hypersubstitutions.U
KW  - n-ary operation
KW  - n-ary term
KW  - superposition of n-ary operations and n-ary
KW  - terms
KW  - linear term
KW  - r-term
KW  - Menger algebra of rank n
KW  - partial Menger
KW  - algebra of rank n
KW  - r-hypersubstitution
Y1  - 2021
U6  - https://doi.org/10.1142/S1793557121500923
SN  - 1793-5571
SN  - 1793-7183
VL  - 14
IS  - 06
PB  - World Scientific
CY  - Singapore
ER  -